On dispersion managed nonlinear Schr\"odinger equations with lumped amplification

TL;DR

This paper proves the global well-posedness and convergence of solutions for a nonlinear Schr"odinger equation with periodic coefficients, relevant to optical-fiber communications, as the small parameter approaches zero.

Contribution

It establishes the well-posedness and asymptotic convergence of solutions for dispersion-managed nonlinear Schr"odinger equations with lumped amplification.

Findings

Proves global well-posedness of the equation.

Shows solutions converge to the averaged Gabitov-Turitsyn equation.

Applicable to optical-fiber communication models.

Abstract

We show the global well-posedness of the nonlinear Schr\"odinger equation with periodically varying coefficients and a small parameter $\varepsilon>0$, which is used in optical-fiber communications. We also prove that the solutions converge to the solution for the Gabitov-Turitsyn or averaged equation as $\varepsilon$ tends to zero.